TY - GEN

T1 - A riemannian-geometry approach for dynamics and control of object manipulation under constraints

AU - Arimoto, Suguru

AU - Yoshida, Morio

AU - Sekimoto, Masahiro

AU - Tahara, Kenji

PY - 2009/11/2

Y1 - 2009/11/2

N2 - A Riemannian-geometry approach for control and stabilization of dynamics of object manipulation under holonomic or non-holonomic (but Pfaffian) constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a nonholonomic constraint is reinterpreted in terms of "submersion" in Riemannian geometry. A force control signal constructed in the image space spanned from the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability on a manifold for a redundant system under holonomic constraints is discussed. Second, control and stabilization of dynamics of two-dimensional object grasping and manipulation by using a pair of multi-joint robot fingers are tackled, when a rigid object is given with arbitrary shape. Then, it is shown that rolling contact constraint induce the Euler equation of motion in an implicit function form, in which constraint forces appear as wrench vectors affecting on the object. The Riemannian metric can be introduced in a natural way on a constraint submanifold induced by rolling contacts. A control signal called "blind grasping" is defined and shown to be effective in stabilization of grasping without using the details of information of object shape and parameters or external sensing. The concept of stability of the closedloop system under constraints is renewed in order to overcome the degrees-of-freedom redundancy problem. An extension of Dirichlet-Lagrange's stability theorem to a system of DOFredundancy under constraints is presented by using a Morse- Lyapunov function.

AB - A Riemannian-geometry approach for control and stabilization of dynamics of object manipulation under holonomic or non-holonomic (but Pfaffian) constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a nonholonomic constraint is reinterpreted in terms of "submersion" in Riemannian geometry. A force control signal constructed in the image space spanned from the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability on a manifold for a redundant system under holonomic constraints is discussed. Second, control and stabilization of dynamics of two-dimensional object grasping and manipulation by using a pair of multi-joint robot fingers are tackled, when a rigid object is given with arbitrary shape. Then, it is shown that rolling contact constraint induce the Euler equation of motion in an implicit function form, in which constraint forces appear as wrench vectors affecting on the object. The Riemannian metric can be introduced in a natural way on a constraint submanifold induced by rolling contacts. A control signal called "blind grasping" is defined and shown to be effective in stabilization of grasping without using the details of information of object shape and parameters or external sensing. The concept of stability of the closedloop system under constraints is renewed in order to overcome the degrees-of-freedom redundancy problem. An extension of Dirichlet-Lagrange's stability theorem to a system of DOFredundancy under constraints is presented by using a Morse- Lyapunov function.

UR - http://www.scopus.com/inward/record.url?scp=70350417297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350417297&partnerID=8YFLogxK

U2 - 10.1109/ROBOT.2009.5152414

DO - 10.1109/ROBOT.2009.5152414

M3 - Conference contribution

AN - SCOPUS:70350417297

SN - 9781424427895

T3 - Proceedings - IEEE International Conference on Robotics and Automation

SP - 1683

EP - 1690

BT - 2009 IEEE International Conference on Robotics and Automation, ICRA '09

T2 - 2009 IEEE International Conference on Robotics and Automation, ICRA '09

Y2 - 12 May 2009 through 17 May 2009

ER -